Question 47: Wave Optics

Question

Two identical light waves, propagating in the
same direction, have a phase difference $$\delta$$. After
they superpose the intensity of the resulting
wave will be proportional to

Accepted Answer

Phase difference between the two identical waves $$=\delta$$
For identical wave,
$$a_1=a_2=a$$
After superposition, intensity of resultant wave
$$\begin{aligned}
I & \propto(	ext { Amplitude })^2 \
& \propto A^2 \
& \propto\left(a_1^2+a_2^2+2 a_1 a_2 \cos \deltaight) \
& \propto\left(a^2+a^2+2 a^2 \cos \deltaight) \
& \propto 2 a^2(1+\cos \delta) \
& \propto 2 a^2 \cdot\left(2 \cos ^2 \frac{\delta}{2}ight) \
& \propto 4 a^2 \cos ^2\left(\frac{\delta}{2}ight) \
\Rightarrow \quad I & \propto \cos ^2\left(\frac{\delta}{2}ight)
\end{aligned}$$

Answer

$$\cos\delta$$

Answer

$$\cos(\delta/2)$$

Answer

$$\cos^2(\delta/2)$$

Answer

$$\cos^2\delta$$

Wave Optics

Two identical light waves, propagating in the same direction, have a phase difference $\delta$. After they superpose the intensity of the resulting wave will be proportional to

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